What is the integral of ye^{x^3} ?

The integral of ye^{x^3} is (e^{x^3}y^2)/2+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ye^{x^3}

\int y e^{x^{3}}

\frac{e ^{x^{3}} y ^{2}}{2} + C

Solution steps

\int y e^{x^{3}} d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= e^{x^{3}} \cdot \int y d y

Apply the Power Rule

: \frac{y ^{2}}{2}

= e^{x^{3}} \frac{y ^{2}}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{e ^{x^{3}} y ^{2}}{2}

Add a constant to the solution

= \frac{e ^{x^{3}} y ^{2}}{2} + C

\int 5 x^{4} e^{5 x^{5}} d x

\int (\frac{x}{x ^{2} - 4}) d x

\int (2 x)^{- \frac{1}{2}} d x

\int e^{2} x^{2} d x

\int \frac{5 - 2 x}{4 + 3 x} d x